- Email: [email protected]
Applying Fuzzy Outranking Method to Measurement System of Multidimensional Performance
Procedia Social and Behavioral Sciences
Available online at www.sciencedirect.com
Procedia - Social and Behavioral Sciences 00 (2011) 000–000 Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
www.elsevier.com/locate/procedia
Applying Fuzzy Outranking Method to Measurement System of Multidimensional Performance Fuyume SAI Department of Business Studies and Informatics, Faculty of Business Administration, Daito Bunka University 1-9-1 Takashimadaira Itabashi-ku Tokyo, 175-8571 Japan Email : [email protected]
Abstract Performance measurement and evaluation are widely conducted in contemporary organizations. The decision-making ambiguity in performance measurement system research has been conceptually studied from accounting, organizational and behavioral perspectives, however it is still not paid major attention, although some fuzzy methodologies have been exploited in measuring and evaluating performance in several practical areas. The aim of this paper is to propose a general system of multidimensional performance evaluation and introduce performance rating into it by applying fuzzy outranking method. By doing this, the performances can be evaluated reciprocally through performance rating from multiperspectives. Moreover, the system can be utilized for measuring and evaluating between divisions or companies. © © 2011 2011 Published Published by by Elsevier Elsevier Ltd. Ltd. Selection Selection and/or and/or peer-review peer-review under under responsibility responsibility of of the the Asia Asia Pacific Pacific Business Innovation and Technology Management Society Business Innovation and Technology Management Society (APBITM).” Keywords: Multidimensional performance, Performance measurement systems, Balanced Scorecard, Fuzzy outranking
1. Introduction Measuring and evaluating business and managerial performance of an organization is a multidimensional and considerably complicated task for managers since they have to balance the objectives of performances against each other and against not only today’s but also tomorrow’s competing demands[19]. Maximization of productivity and efficiency has been the major pursuit for the Taylorian organization in the industrial age, and the performance expression was financial usually with using the lagging measures such as standard cost ratios e.g. productivity ratios per month or the turnover per year. Financial and linear operators played the leading role in the performance measurement system for taking the appropriate action to improve productivity and increase efficiency. Afterward, performance measurement and evaluation become multicriteria, technical criteria was combined into financial criteria from such viewpoints as quality, delivery for pursuing effective cost-reduction through improving 1877-0428 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Asia Pacific Business Innovation and Technology Management Society doi:10.1016/j.sbspro.2011.10.553
346
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
operational performance. As in the representative management methodologies at that time, there is no doubt that total quality control and value engineering can be recalled. Achievement of the necessary product function from the viewpoint of customer was added into the management control crossing multiple units: financial, procuring, engineering, marketing. Engineering, procuring and marketing are involved in the analysis process to define the priority requirements from customer’s standpoint[4][16]. The target selling price, margins, and market share have been the leading measures. Nowadays, the view of “you can’t manage without measuring, and what is measured gets done” is undeniable[8][9][10][15]. More and more sophisticated performance measurement systems for picturing more comprehensive portrait of organization related strategy objectives have been developed and exploited in practical area[18][14][13]. Meanwhile, the focus of the performance measurement and evaluation has shifted from cost-reduction to growth in recent years[3]. Among the be-used performance measurement systems, balanced scorecard (BSC) is the most popular one which is also the 6th of top 10 management tools in 2010[3]. In BSC, performance measures are grouped into four categories: financial, customer, internal process and learning and growth, and performance measurement and evaluation are balanced from the four perspectives (categories). BSC consists mainly of the following processes[6][7][8][15]: recognizing organization architecture; defining strategy objective; selecting measures; and building implementation plan. Defining strategy objective and selecting measures are the core decision-making process in the system since strategy and vision of organization are understood, articulated and translated into a set of financial and non-financial measures and into a causal model with a step-by-step sequence of cause-and-effect relationships leading from the most fundamental aspects of performance to financial performance. The casual links between categories are hypothesized, that is, strong learning and growth leads to improved internal processes, improved internal processes lead to increased customer satisfaction, and increases in customer satisfaction leads to improved financial performance. Clearly, how to reflect the decision-makers’ subjective understanding or insight rationally, and how to evaluate the relations among the measures effectively and efficiently should be essential and indispensable subject of measuring and evaluating performance[1][17][20], but they are often ignored somewhat for balancing the complexity and apperception, in other words, people in practice often keep away from evaluation of intangible substance such as human insight, beliefs, or understandings. The decision-making ambiguity in BSC mentioned above has being conceptually studied within accounting, organizational and behavioral perspectives, and has been dealt with by applying fuzzy methodologies in several practical areas[11][14][13][21]. However, it is still not paid major attention in performance measurement research. This paper aims to introduce performance rating into the multidimensional performance measurement system[5] by using fuzzy outranking method for performance evaluation. The rest of the paper is organized as follows: first, the measurement and evaluation system of multidimensional performance is described in the following section, and the next section will propose a method for ranking the performance from multiple perspectives under the consideration for dealing with the decision-making ambiguity. An illustrative example shows how to use the method. Finally, a conclusion is discussed at the end. 2. The measurement and evaluation System of multidimentional performance In this section, a BSC–based multidimensional performance measurement system[5] is described and shown in figure 1. It starts from the initial stage, termed structural modeling, at which four perspective models (financial, customer, internal business process, and organization learning) are built up respectively through the processes encircled within the dotted line in the left side of figure 1. We also see it as multidimensional system analysis. In order to obtain a concrete model of the respective perspective, fuzzy structural modeling method[17] is applied to portray an intuitive graphical hierarchy with well-preserved
347
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
contextual relations among measurement elements. Firstly, evaluators’ mental model (imagination) of the given problem are embedded and reflected on a structural model. Here, the measurement elements are specified by techniques such as nominal group techniques, questionnaire or interview according to the operational conditions. Then, the contextual relations among the elements are examined and represented based on the assumption of cause-and-effect. And the hierarchy of measurement system is constructed and drawn as an interpretive structural model. Furthermore, In order to compare the structural model with the mental model, a feedback for learning will be conducted by evaluators[22]. If an agreement among evaluators is obtained, then the process goes up to the next stage, and the result is set as the outcome of stage A. Otherwise, the modeling process restarts from the embedding process or from drawing out and representing the evaluating elements process. Then the process goes as same as illustrated in figure 1 until a consenting structural model is obtained. As the outcome of stage A, the models of perspectives are obtained, which are evaluated respectively so as to obtain each evaluation value of each perspective model. Further, an integrated value is computed at stage C. At both of evaluating and integrating stage, multiple attributes decision making and/or fuzzy inference mechanism can be introduced for achieving the simultaneous optimization of multiple elements of system for determination of a satisfying solution to a given problem[23]. In addition, fuzzy outranking method is proposed to evaluate performance through performance rating at both stages in this paper in order to give the system a ranking function. Then if the evaluation value is valid, the process goes to the end, otherwise, a feedback will be conducted at stage D, back to the stage B or A, performed until a consenting integrated result is derived. Stage A: Structural Modeling
Stage B: Evaluating
Stage C: Integrating
Stage Ｄ:Verifying
Structural modeling of the perspective (Finance, Customer, Internal Process, Learning and Growth)
Evaluating with four structural models
Integrating the values of the four perspectives
Verifying the validity of the integrated evaluation value
Start Evaluating by using the structural models:
Imagining the perspective no Consensus Embedding and reflecting Embedding and reflecting
yes
Financial model
Computing Integrated Evaluation values
Customer model
Is the integrated value valid ?
yes
Stop
Internal Process model Learning and Growth model
Constructing structural model of the perspective
Applying
Applying
Drawing out and representing the relations among elements
No
(1) Multiple Attributes Decision Making (2) Fuzzy Inference Mechanism (3) Fuzzy Outranking
Feedback
Figure 1 The BSC-based multidimensional performance measurement system
3. The fuzzy outranking method The method to roughly compare two alternatives a and with loose relation, which means a is at least as good as a’ or a is not worse than , it says that a outranks . Reversely, If is evaluated better than a or they are incomparable to each other, it says that a dose not outrank . These relations are valued as 0 or 1 in the traditional outranking method[2], that is, a outranks = 1 and = 0 if a dose not outrank . In fuzzy outranking method[12], the outranking degree is valued between 0 and 1. More precisely, the degree is determined with a fuzzy membership function by using an indifference threshold and a preference threshold , where i represents one of evaluating criteria. Thus
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Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
the corresponding value is denoted by , and they are aggregated by a weighted average with a set of weight , and called concordance index denoted by Another index is called discordance index denoted by , which is constructed by using a fuzzy set with the preference threshold and a veto threshold . This index represents the degree of discordance with the superiority of a over '. Thus = 1 implies that the “a outranks ” is exclusively vetoed from the number j point of view. If there are discordance points of view j1, …, jk, whose index are greater than , then the total outranking index is calculated by the following formula, . According to the total outranking index , the performance rating is calculated by ELECTRE III[2]’s algorithm through building descending ranking and ascending ranking. 4. An illustrative example Consider that there are four companies whose performance is evaluated from four perspectives: financial, customer, internal process, and learning and growth, denoted by respectively. With the limit of paper space, how to obtain the evaluation values of each perspective of each company from stage B of the system described in the second section are not shown in this section, only the evaluation values are shown in table 1 In this case, the weights of each perspective evaluation, the preference threshold, the indifference threshold, and the veto threshold are set as follows: wi={0.35, 0.30, 0.20, 0.15} (i=1,2,3,4), pi= 0.1 (i=1,2,3,4), qi= 0.05 (i=1,2,3,4), vi= 0.2, (i=1,2,3,4), and the calculation results are shown in the following tables respectively. Table 1 The evaluation value of each company from the four perspectives
0.526
0.638
0.736
0.549
0.724
0.534
0.512
0.493
0.637
0.739
0.436
0.443
0.423
0.495
0.675
0.598
Table 2 The corresponding value for each criterion
1
0
0
1
1
1
1
1
1
0.26
1
1
0
0
0
1
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Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0.48
1
0
0.78
1
1
1
1
1
1
1
0.88
1
1
0
0
1
1
0
1
1
1
1
Table 3 The concordance index
1
0.65
0.35
1
0.48
1
0.70
0.65
0.65
0.64
1
0.65
0.31
0.35
0.35
1
Table 4 The discordance indices
0
0.98
0.11
0
0
0
0
0.
0
0
0
0
0.03
1
1
0
0
0
0.01
0
0.04
0
1
0
0
0
0
0
0.43
0
1
0
350
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
0
0
0
0
1
0
0
0.63
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0.05
0.06
0
0
1
0
0
0
0
-
0.04
0.35
1
0
-
0
0.65
0
0.64
-
0
0.26
0
0
-
Table 5 The total outranking index
Table 6 Performance rating result
ranking
the result
ascending
→
→
→
descending
←
←
←
5. Conclusive discussion In today’s business environment, performance measurement has been becoming more and more complicated, and its focus has shifted from cost-reduction to growth. This paper adopts the pragmatic standpoint, that is, despite the complexities and ambiguity in the decision-making regarding performance measurement systems, performance is measured and measurement and evaluation are widely used in contemporary organizations. In this paper, a system for measuring and evaluating multiple performances on basis of BSC was proposed, and further, introduced fuzzy outranking method into it for evaluating performances. A simple example was illustrated to show the validity of fuzzy outranking method in the proposed system. However how to use the proposed system with the other methods to simulate practical situation remain at this time, and it will be undertook in the future.
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
References [1] Andrew Likierman,”The Five Traps of Performance Measurement”, Harvard Business Review, pp.96101, October, 2009. [2] B. Roy, Multicriteria Methodology for Decision Aiding, Kluwer Academic Publishers, Dordrecht, 1996. [3] Darrel K. Rigby, Management Tools 2011: An Executive’s Guide, Bain & Company, 2011. [4] Dongmei, C. and Michio, A., Value Engineering Concept Based on Fuzzy Theory, Proceedings of the 3rd Asia-Pacific Conference on Industrial Engineering and Management Systems, pp. 482-487, 2000. [5] Dongmei, C., Amagasa, M., Suzuki, K., and Matsuo, T., A Multidimensional Measurement System With Balanced Score Card, Proceedings of the 38th Annual Meeting Decision Science Institute, pp.5061/5083, 2007. [6] Kaplan, R.S. and Norton, D.P., The Balanced Scorecard：measures that drive performance”, Harvard Business Review, Vol.70, No.1, January-February, pp71-79, 1992. [7] Kaplan, R.S. and Norton, D.P., “Putting the balanced scorecard to work”. Harvard Business Review, September-October, pp134-147, 1993. [8] Kaplan, R.S. and Norton, David P., “Using the Balanced Scorecard as a strategic management system”, Harvard Business Review, January-February, pp75-85, 1996. [9] Kaplan, Robert S. and Norton, David P., The Balanced Scorecard: translating strategy into action. Boston Massachusetts, Harvard Business School Press, 1996. [10] Kaplan, Robert S. and Norton, D. P., Alignment : Using the Balanced Scorecard to Create Corporate Synergies, Harvard Business School Press, 2006. [11] Khim Kelly, “Accuracy of Relative Weights on Multiple Leading Performance Measures: Effects on Managerial Performance and Knowledge”, Contemporary Accounting Research, Vol. 27, No. 2, pp. 577608, Summer 2010. [12] Klir J. George and Yuan Bo, Fuzzy Sets and Fuzzy Logic-Theory and Application, Prentice Hall InternationalInc, pp124-132, 1995. [13] Maurice Gosselin, “Designing and Implementing a Performance Measurement System”, CMA Management, pp.15-18, November, 2010. [14] Mattias Elg and Beata Kollberg, “Alternative Argument and Directions for Studying Performance Measurement”, Total Quality Management, Vol.20, No.4, pp. 409-421, Apirl 2009. [15] Michael Hammer, “The 7 Deadly Sins of Performance Measurement”, MIT Sloan Management Review, pp.19-28, Spring, 2007. [16] Michio, A. and Dongmei, C., Establishment of Manufacturing Cost Target by Weight Analysis with Design Parameters, Proceedings of the 6th Asia-Pacific Decision Sciences Institute Conference, pp.1-8, 2001. [17] Nagata, K., Umezawa, M., Cui, D., and Amagasa, M., “Modified Structural Modeling Method and Its Application-Behavior Analysis of passengers for East Japan Railway Company-”, Journal of Industrial Engineering and Management Systems, Vol.7, No. 3, pp. 245-256, 2008.
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[18] Neely, A., Gregory, M. and Platts, K., “Performance Measurement System Design: a literature review and research agenda”, International Journal of Operations Production Management, Vol.15, pp.80-116, 1995. [19] Peter F. Drucker, Management: Tasks, Responsibilities, Practices, HarperBusiness Edition, pp.49-58, 1993. [20] Stephen L. Liedtka, Bryan K. Church and Manash R. Ray, “Performance Variability, Ambiguity Intolerance, and Balanced Scorecard-Based Performance Assessment”, Behavioral Research in Accounting, Vol. 20, No. 2, pp.73-88, 2008. [21] Tseng M.L. (Jan. 2011) Using a hybrid MCDM model to evaluate firm environmental knowledge management in uncertainty. Applied Soft Computing 11(1), 1340~1352 [22] Tseng M.L. (2011) Importance-performance analysis on municipal solid waste management in uncertainty. Environmental Monitoring and Assessment 172(1-4), 171-187 [23] William B. Tayler, “The Balanced Scorecard as a Strategy-Evaluation Tool: The Effects of Implementation Involvement and a Causal-Chain Focus”, The Accounting Review, Vol.85, No.3, pp. 1095-1117, 2010.
Available online at www.sciencedirect.com
Procedia - Social and Behavioral Sciences 00 (2011) 000–000 Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
www.elsevier.com/locate/procedia
Applying Fuzzy Outranking Method to Measurement System of Multidimensional Performance Fuyume SAI Department of Business Studies and Informatics, Faculty of Business Administration, Daito Bunka University 1-9-1 Takashimadaira Itabashi-ku Tokyo, 175-8571 Japan Email : [email protected]
Abstract Performance measurement and evaluation are widely conducted in contemporary organizations. The decision-making ambiguity in performance measurement system research has been conceptually studied from accounting, organizational and behavioral perspectives, however it is still not paid major attention, although some fuzzy methodologies have been exploited in measuring and evaluating performance in several practical areas. The aim of this paper is to propose a general system of multidimensional performance evaluation and introduce performance rating into it by applying fuzzy outranking method. By doing this, the performances can be evaluated reciprocally through performance rating from multiperspectives. Moreover, the system can be utilized for measuring and evaluating between divisions or companies. © © 2011 2011 Published Published by by Elsevier Elsevier Ltd. Ltd. Selection Selection and/or and/or peer-review peer-review under under responsibility responsibility of of the the Asia Asia Pacific Pacific Business Innovation and Technology Management Society Business Innovation and Technology Management Society (APBITM).” Keywords: Multidimensional performance, Performance measurement systems, Balanced Scorecard, Fuzzy outranking
1. Introduction Measuring and evaluating business and managerial performance of an organization is a multidimensional and considerably complicated task for managers since they have to balance the objectives of performances against each other and against not only today’s but also tomorrow’s competing demands[19]. Maximization of productivity and efficiency has been the major pursuit for the Taylorian organization in the industrial age, and the performance expression was financial usually with using the lagging measures such as standard cost ratios e.g. productivity ratios per month or the turnover per year. Financial and linear operators played the leading role in the performance measurement system for taking the appropriate action to improve productivity and increase efficiency. Afterward, performance measurement and evaluation become multicriteria, technical criteria was combined into financial criteria from such viewpoints as quality, delivery for pursuing effective cost-reduction through improving 1877-0428 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Asia Pacific Business Innovation and Technology Management Society doi:10.1016/j.sbspro.2011.10.553
346
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
operational performance. As in the representative management methodologies at that time, there is no doubt that total quality control and value engineering can be recalled. Achievement of the necessary product function from the viewpoint of customer was added into the management control crossing multiple units: financial, procuring, engineering, marketing. Engineering, procuring and marketing are involved in the analysis process to define the priority requirements from customer’s standpoint[4][16]. The target selling price, margins, and market share have been the leading measures. Nowadays, the view of “you can’t manage without measuring, and what is measured gets done” is undeniable[8][9][10][15]. More and more sophisticated performance measurement systems for picturing more comprehensive portrait of organization related strategy objectives have been developed and exploited in practical area[18][14][13]. Meanwhile, the focus of the performance measurement and evaluation has shifted from cost-reduction to growth in recent years[3]. Among the be-used performance measurement systems, balanced scorecard (BSC) is the most popular one which is also the 6th of top 10 management tools in 2010[3]. In BSC, performance measures are grouped into four categories: financial, customer, internal process and learning and growth, and performance measurement and evaluation are balanced from the four perspectives (categories). BSC consists mainly of the following processes[6][7][8][15]: recognizing organization architecture; defining strategy objective; selecting measures; and building implementation plan. Defining strategy objective and selecting measures are the core decision-making process in the system since strategy and vision of organization are understood, articulated and translated into a set of financial and non-financial measures and into a causal model with a step-by-step sequence of cause-and-effect relationships leading from the most fundamental aspects of performance to financial performance. The casual links between categories are hypothesized, that is, strong learning and growth leads to improved internal processes, improved internal processes lead to increased customer satisfaction, and increases in customer satisfaction leads to improved financial performance. Clearly, how to reflect the decision-makers’ subjective understanding or insight rationally, and how to evaluate the relations among the measures effectively and efficiently should be essential and indispensable subject of measuring and evaluating performance[1][17][20], but they are often ignored somewhat for balancing the complexity and apperception, in other words, people in practice often keep away from evaluation of intangible substance such as human insight, beliefs, or understandings. The decision-making ambiguity in BSC mentioned above has being conceptually studied within accounting, organizational and behavioral perspectives, and has been dealt with by applying fuzzy methodologies in several practical areas[11][14][13][21]. However, it is still not paid major attention in performance measurement research. This paper aims to introduce performance rating into the multidimensional performance measurement system[5] by using fuzzy outranking method for performance evaluation. The rest of the paper is organized as follows: first, the measurement and evaluation system of multidimensional performance is described in the following section, and the next section will propose a method for ranking the performance from multiple perspectives under the consideration for dealing with the decision-making ambiguity. An illustrative example shows how to use the method. Finally, a conclusion is discussed at the end. 2. The measurement and evaluation System of multidimentional performance In this section, a BSC–based multidimensional performance measurement system[5] is described and shown in figure 1. It starts from the initial stage, termed structural modeling, at which four perspective models (financial, customer, internal business process, and organization learning) are built up respectively through the processes encircled within the dotted line in the left side of figure 1. We also see it as multidimensional system analysis. In order to obtain a concrete model of the respective perspective, fuzzy structural modeling method[17] is applied to portray an intuitive graphical hierarchy with well-preserved
347
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
contextual relations among measurement elements. Firstly, evaluators’ mental model (imagination) of the given problem are embedded and reflected on a structural model. Here, the measurement elements are specified by techniques such as nominal group techniques, questionnaire or interview according to the operational conditions. Then, the contextual relations among the elements are examined and represented based on the assumption of cause-and-effect. And the hierarchy of measurement system is constructed and drawn as an interpretive structural model. Furthermore, In order to compare the structural model with the mental model, a feedback for learning will be conducted by evaluators[22]. If an agreement among evaluators is obtained, then the process goes up to the next stage, and the result is set as the outcome of stage A. Otherwise, the modeling process restarts from the embedding process or from drawing out and representing the evaluating elements process. Then the process goes as same as illustrated in figure 1 until a consenting structural model is obtained. As the outcome of stage A, the models of perspectives are obtained, which are evaluated respectively so as to obtain each evaluation value of each perspective model. Further, an integrated value is computed at stage C. At both of evaluating and integrating stage, multiple attributes decision making and/or fuzzy inference mechanism can be introduced for achieving the simultaneous optimization of multiple elements of system for determination of a satisfying solution to a given problem[23]. In addition, fuzzy outranking method is proposed to evaluate performance through performance rating at both stages in this paper in order to give the system a ranking function. Then if the evaluation value is valid, the process goes to the end, otherwise, a feedback will be conducted at stage D, back to the stage B or A, performed until a consenting integrated result is derived. Stage A: Structural Modeling
Stage B: Evaluating
Stage C: Integrating
Stage Ｄ:Verifying
Structural modeling of the perspective (Finance, Customer, Internal Process, Learning and Growth)
Evaluating with four structural models
Integrating the values of the four perspectives
Verifying the validity of the integrated evaluation value
Start Evaluating by using the structural models:
Imagining the perspective no Consensus Embedding and reflecting Embedding and reflecting
yes
Financial model
Computing Integrated Evaluation values
Customer model
Is the integrated value valid ?
yes
Stop
Internal Process model Learning and Growth model
Constructing structural model of the perspective
Applying
Applying
Drawing out and representing the relations among elements
No
(1) Multiple Attributes Decision Making (2) Fuzzy Inference Mechanism (3) Fuzzy Outranking
Feedback
Figure 1 The BSC-based multidimensional performance measurement system
3. The fuzzy outranking method The method to roughly compare two alternatives a and with loose relation, which means a is at least as good as a’ or a is not worse than , it says that a outranks . Reversely, If is evaluated better than a or they are incomparable to each other, it says that a dose not outrank . These relations are valued as 0 or 1 in the traditional outranking method[2], that is, a outranks = 1 and = 0 if a dose not outrank . In fuzzy outranking method[12], the outranking degree is valued between 0 and 1. More precisely, the degree is determined with a fuzzy membership function by using an indifference threshold and a preference threshold , where i represents one of evaluating criteria. Thus
348
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
the corresponding value is denoted by , and they are aggregated by a weighted average with a set of weight , and called concordance index denoted by Another index is called discordance index denoted by , which is constructed by using a fuzzy set with the preference threshold and a veto threshold . This index represents the degree of discordance with the superiority of a over '. Thus = 1 implies that the “a outranks ” is exclusively vetoed from the number j point of view. If there are discordance points of view j1, …, jk, whose index are greater than , then the total outranking index is calculated by the following formula, . According to the total outranking index , the performance rating is calculated by ELECTRE III[2]’s algorithm through building descending ranking and ascending ranking. 4. An illustrative example Consider that there are four companies whose performance is evaluated from four perspectives: financial, customer, internal process, and learning and growth, denoted by respectively. With the limit of paper space, how to obtain the evaluation values of each perspective of each company from stage B of the system described in the second section are not shown in this section, only the evaluation values are shown in table 1 In this case, the weights of each perspective evaluation, the preference threshold, the indifference threshold, and the veto threshold are set as follows: wi={0.35, 0.30, 0.20, 0.15} (i=1,2,3,4), pi= 0.1 (i=1,2,3,4), qi= 0.05 (i=1,2,3,4), vi= 0.2, (i=1,2,3,4), and the calculation results are shown in the following tables respectively. Table 1 The evaluation value of each company from the four perspectives
0.526
0.638
0.736
0.549
0.724
0.534
0.512
0.493
0.637
0.739
0.436
0.443
0.423
0.495
0.675
0.598
Table 2 The corresponding value for each criterion
1
0
0
1
1
1
1
1
1
0.26
1
1
0
0
0
1
349
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0.48
1
0
0.78
1
1
1
1
1
1
1
0.88
1
1
0
0
1
1
0
1
1
1
1
Table 3 The concordance index
1
0.65
0.35
1
0.48
1
0.70
0.65
0.65
0.64
1
0.65
0.31
0.35
0.35
1
Table 4 The discordance indices
0
0.98
0.11
0
0
0
0
0.
0
0
0
0
0.03
1
1
0
0
0
0.01
0
0.04
0
1
0
0
0
0
0
0.43
0
1
0
350
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
0
0
0
0
1
0
0
0.63
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0.05
0.06
0
0
1
0
0
0
0
-
0.04
0.35
1
0
-
0
0.65
0
0.64
-
0
0.26
0
0
-
Table 5 The total outranking index
Table 6 Performance rating result
ranking
the result
ascending
→
→
→
descending
←
←
←
5. Conclusive discussion In today’s business environment, performance measurement has been becoming more and more complicated, and its focus has shifted from cost-reduction to growth. This paper adopts the pragmatic standpoint, that is, despite the complexities and ambiguity in the decision-making regarding performance measurement systems, performance is measured and measurement and evaluation are widely used in contemporary organizations. In this paper, a system for measuring and evaluating multiple performances on basis of BSC was proposed, and further, introduced fuzzy outranking method into it for evaluating performances. A simple example was illustrated to show the validity of fuzzy outranking method in the proposed system. However how to use the proposed system with the other methods to simulate practical situation remain at this time, and it will be undertook in the future.
Fuyume SAI / Procedia - Social and Behavioral Sciences 25 (2011) 345 – 352
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